Energy Gaps in Etched Graphene Nanoribbons

Starting from a tight-binding model, we derive the energy gaps induced by intrinsic spin-orbit (ISO) coupling in the low-energy band structures of graphene nanoribbons. The armchair graphene nanoribbons may be either semiconducting or metallic, depending on their widths in the absence of ISO interactions. For the metallic ones, the gaps induced by ISO coupling decrease with increasing ribbon widths. For the ISO interactions, we find that zigzag graphene nanoribbons with odd chains still have no band gaps while those with even chains have gaps with a monotonic decreasing dependence on the widths. First-principles calculations have also been carried out, verifying the results of the tight-binding approximation. Our paper reveals that the ISO interaction of graphene nanoribbons is governed by their geometrical parameters.

Download Full-text

Energy gaps in zero-dimensional graphene nanoribbons

Applied Physics Letters ◽

10.1063/1.2761531 ◽

2007 ◽

Vol 91 (4) ◽

pp. 042101 ◽

Cited By ~ 113

Author(s):

Philip Shemella ◽

Yiming Zhang ◽

Mitch Mailman ◽

Pulickel M. Ajayan ◽

Saroj K. Nayak

Keyword(s):

Graphene Nanoribbons ◽

Energy Gaps

Download Full-text

Electronic Properties of Graphene Nanoribbons Doped with Pyrrole-Like Nitrogen

Proceedings of Universities ELECTRONICS ◽

10.24151/1561-5405-2021-26-6-447-458 ◽

2021 ◽

Vol 26 (6) ◽

pp. 447-458

Author(s):

V.V. Shunaev ◽

◽

A.Yu. Gerasimenko ◽

O.E. Glukhova ◽

◽

...

Keyword(s):

Band Structure ◽

Graphene Nanoribbons ◽

Chemical Elements ◽

Electronic Devices ◽

Zigzag Edge ◽

Atomic Lattice ◽

Nitrogen Doped ◽

Energy Gaps ◽

The Relationship ◽

Zigzag Graphene Nanoribbons

Doping of graphene nanoribbons with various chemical elements leads to a change in their band structure, which significantly expands the range of applications of these objects in modern electronic devices. In this work, the authors investigate graphene nanoribbons of the «armchair» and «zigzag» types with different concentrations of pyrrole-like nitrogen at the edges. The SCC-DFTB method was used to establish the most energetically favorable configurations of pyrrole-like nitrogen at each edge of graphene nanoribbons. The relationship between the energy gaps of graphene nanoribbons and the content of the considered functional nitrogen-containing groups in them was determined. Calculations have shown that, by incorporating into the atomic lattice, pyrrole-like nitrogen at the «zigzag» edge transfers a greater amount of charge to nearby carbon atoms, which makes such nanoribbons more chemically active in comparison with «armchair» type nanoribbons. Nitrogen doped «zigzag» graphene nanoribbons may be a promising chemoresistive element of nanosensors; however, these conclusions require further calculations.

Download Full-text

Effects of edge magnetism and external electric field on energy gaps in multilayer graphene nanoribbons

Physical Review B ◽

10.1103/physrevb.82.115426 ◽

2010 ◽

Vol 82 (11) ◽

Cited By ~ 29

Author(s):

Bhagawan Sahu ◽

Hongki Min ◽

Sanjay K. Banerjee

Keyword(s):

Electric Field ◽

External Electric Field ◽

Graphene Nanoribbons ◽

Multilayer Graphene ◽

Energy Gaps

Download Full-text

Bandgaps of Atomically Precise Graphene Nanoribbons and Occam’s Razor

10.33774/chemrxiv-2021-6pkjq ◽

2021 ◽

Author(s):

Aristides Zdetsis

Keyword(s):

Graphene Nanoribbons ◽

Primary Source ◽

Edge States ◽

General Symmetry ◽

Tddft Calculations ◽

Energy Gaps ◽

Symmetry Principles ◽

Unambiguous Detection ◽

Dft And Tddft Calculations ◽

Substrate Influence

Rationalization of energy gaps of atomically precise AGNRs, “bulk” (ΔΕac) or “zigzag-end” (ΔΕzz), could be challenging and controversial concerning their magnitude, origin, substrate influence (ΔΕsb), and spin-polarization, among others. Hereby, a simple self-consistent and “economical” interpretation is presented, based on “appropriate” DFT (and TDDFT) calculations, general symmetry principles, and plausibility arguments, which is fully consistent with current experimental measurements for 5-, 7-, and 9-AGNRs within less than 1%, although at variance with some prevailing views or interpretations for ΔΕac, ΔΕzz, and ΔΕsb. Thus, an excellent agreement between experiment and theory emerges, provided some established stereotypes are reconsidered and/or abandoned. The primary source of discrepancies is the finite length of AGNRs together with inversion-symmetry conflict and topological end/edge states, which invariably mix with other “bulk” states making their unambiguous detection/distinction difficult. This can be further tested by eliminating end-states (and ΔΕzz), by eliminating empty (non-aromatic) end-rings

Download Full-text

Energy Gaps in Graphene Nanoribbons

Physical Review Letters ◽

10.1103/physrevlett.97.216803 ◽

2006 ◽

Vol 97 (21) ◽

Cited By ~ 3572

Author(s):

Young-Woo Son ◽

Marvin L. Cohen ◽

Steven G. Louie

Keyword(s):

Graphene Nanoribbons ◽

Energy Gaps

Download Full-text

Feature-Rich Geometric and Electronic Properties of Carbon Nanoscrolls

Nanomaterials ◽

10.3390/nano11061372 ◽

2021 ◽

Vol 11 (6) ◽

pp. 1372

Author(s):

Shih-Yang Lin ◽

Sheng-Lin Chang ◽

Cheng-Ru Chiang ◽

Wei-Bang Li ◽

Hsin-Yi Liu ◽

...

Keyword(s):

First Principles ◽

Graphene Nanoribbons ◽

Finite Size ◽

Ribbon Width ◽

Energy Gaps ◽

Atomic Interactions ◽

Essential Properties ◽

Carbon Nanoscrolls ◽

Spin Degeneracy ◽

Geometric And Electronic Properties

How to form carbon nanoscrolls with non-uniform curvatures is worthy of a detailed investigation. The first-principles method is suitable for studying the combined effects due to the finite-size confinement, the edge-dependent interactions, the interlayer atomic interactions, the mechanical strains, and the magnetic configurations. The complex mechanisms can induce unusual essential properties, e.g., the optimal structures, magnetism, band gaps and energy dispersions. To reach a stable spiral profile, the requirements on the critical nanoribbon width and overlapping length will be thoroughly explored by evaluating the width-dependent scrolling energies. A comparison of formation energy between armchair and zigzag nanoscrolls is useful in understanding the experimental characterizations. The spin-up and spin-down distributions near the zigzag edges are examined for their magnetic environments. This accounts for the conservation or destruction of spin degeneracy. The various curved surfaces on a relaxed nanoscroll will create complicated multi-orbital hybridizations so that the low-lying energy dispersions and energy gaps are expected to be very sensitive to ribbon width, especially for those of armchair systems. Finally, the planar, curved, folded, and scrolled graphene nanoribbons are compared with one another to illustrate the geometry-induced diversity.

Download Full-text